4 Answers
4

Dreams are essentially a lower-prophecy that anyone can receive. In the Torah, many people experience dreams with messages, Yaakov, Yosef, Pharoh and his wine-maker and baker, Avimelech, Ballaam.

Talmud Bruchos 55a-57b has a bunch to say about dreams and how to interpret certain symbols in dreams.

Dreams are 1/60th of a prophecy.

Part of them is nonsense. "Just as wheat cannot be without straw, so there cannot be a dream without some nonsense" (55a)

"A dream which is not interpreted is like a letter which is not read." (55a)

A good dream can take as long as 22 years to be fulfilled. (55b)

(and much more)

on Interpreting Dreams: A dream is not inherently good or bad. "All dreams follow the mouth"(55b), if the interpreter interprets the dream as good, it will be good, if they interpret it as bad it's bad. As such, one should always try to interpret a dream as good. Bar Hedya would give positive interpretations only to those who paid him, and unfavorable interpretations to those who didn't. (56a)

Birkat Kohanim has a paragraph to pray for a positive-conversion of a dream you dreamt and you don't remember. (55b)

Part of the functions of the imaginative faculty is, as you well
know, to retain impressions by the senses, to combine them, and
chiefly to form images. The principal and highest function is
performed when the senses are at rest and pause in their action, for
then it receives, to some extent, divine inspiration in the measure
as it is predisposed for this influence. This is the nature of those
dreams which prove true, and also of prophecy, the difference
being one of quantity, not of quality. Thus our Sages say, that
dream is the sixtieth part of prophecy: and no such comparison
could be made between two things of different kinds, for we
cannot say the perfection of man is so many times the perfection of
a horse. In Bereshit Rabba (sect. xvii.) the following saying of our
Sages occurs," Dream is the nobelet (the unripe fruit) of
prophecy." This is an excellent comparison, for the unripe fruit
(nohelet) is really the fruit to some extent, only it has fallen from
the tree before it was fully developed and ripe. In a similar manner
the action of the imaginative faculty during sleep is the same as at
the time when it receives a prophecy, only in the first case it is not
fully developed, and has not yet reached its highest degree. But
why need I quote the words of our Sages, when I can refer to the
following passage of Scripture :" If there be among you a prophet,
I, the Lord, will make myself known unto him in a vision, in a
dream will I speak to him" (Num. xii. 6). Here the Lord tells us
what the real essence of prophecy is, that it is a perfection acquired
in a dream or in a vision (the original mareh is a noun derived
from the verb raah): the imaginative faculty acquires such an
efficiency in its action that it sees the thing as if it came from
without, and perceives it as if through the medium of bodily
senses. These two modes of prophecy, vision and dream, include
all its different degrees. It is a well-known fact that the thing
which engages greatly and earnestly man's attention whilst he is
awake and in the full possession of his senses forms during his
sleep the object of the action of his imaginative faculty.
Imagination is then only influenced by the intellect in so far as it is
predisposed for such influence. It would be quite useless to
illustrate this by a simile, or to explain it fully, as it is clear, and
every one knows it. It is like the action of the senses, the existence
of which no person with common sense would ever deny.

TalmudBerachot 55b records an opinion that one's dreams are merely a reflection of what one is thinking during the day. Thus:

R. Samuel b. Nahmani said in the name of R. Jonathan: A man is shown in a dream only what is suggested by his own thoughts, as it says, As for thee, Oh King, thy thoughts came into thy mind upon thy bed.37 Or if you like, I can derive it from here: That thou mayest know the thoughts of the heart.38 Raba said: This is proved by the fact that a man is never shown in a dream a date palm of gold, or an elephant going through the eye of a needle.39

And on the next amud:

The Emperor [of Rome]1 said to R. Joshua b. R. Hananyah: You [Jews] profess to be very clever. Tell me what I shall see in my dream. He said to him: You will see the Persians2 making you do forced labour, and despoiling you and making you feed unclean animals with a golden crook. He thought about it all day, and in the night he saw it in his dream.3 King Shapor [I] once said to Samuel: You [Jews] profess to be very clever. Tell me what I shall see in my dream. He said to him: You will see the Romans coming and taking you captive and making you grind date-stones in a golden mill. He thought about it the whole day and in the night saw it in a dream.

Such dreams would not seem to be prophetic.

Abarbaneldiscusses how some dreams are purely the result of the imaginative faculties, modified by the body's physical state, based on the four humors. Thus:

for a person, many times, dreams dreams which have no meaningful substance, and they are the product of the imaginative faculties as it changes because of the temperment. For when the red humor {=blood} prevails, he will dream as if he were cast into a powerful fire. And when the white humor {=phlegm} prevails, he will dream that he has fallen into mighty waters. And the like to this, such that the doctors at times take these dreams as signs as to the nature of the illness.

Of course, Abarbanel held that certain dreams were prophetic in nature. And of course, there are other views encoded in the Talmud, in close proximity, as reflected in other answers on this page.

But I think the most comprehensive answer would be that it is a machlokes; that there were rationalists and non-rationalists even during the time of the Amoraim; that in the time of the Talmud, dream interpretation was regarded as a science, and that this might change as our understanding of science changes.

So, to address the question as posed,

Are they in any way binding, or are they assumed to be just products of an overactive imagination?

The other answers were very good, but if you want a lot of information, I recommend the book
Mishnat HaChalomot by Rabbo Boaz Shalom.
Rab Yehuda Fetaya (ZSWQ"L) (60-70 years ago) wrote that dreams don't mean anything any more, only under very specific circumstances. The Sefer Hassidim (700 years ago) also write this. I heard HaRab Boaz Shalom Shlit"a say in his speech that even if the dream meant something, there really is nobody in our time who can interpret it. In conclusion, quoting one of the Rabbanim of Lublin, he said that dreams are the inner deepest desires of the heart coming into fruition in a dream. Thus, dreams should not be taken seriously as much as they used in the time of the Gemara. I really recommend this book, it is very insightful with 750 pages and discussions on demons, dreams, ayin hara, and all that stuff.

We believe in dreams, as we see by Paaroh, and as we see there is such a thing as a Taanus Chalom - which is a fast when someone has a bad dream. At the same time the Gemara in Berachos 55:2 says that most dreams are from the thoughts we have. The Posuk in Zecharya 10:2 says וַחֲלֹמוֹת הַשָּׁוְא יְדַבֵּרוּ which means they have no meaning. I do not remember who says this, however there seems to be a difference whether an Angel or a demon showed us the dream. How to know the difference I do not know.

It's from Berachos 55b: "When Samuel had a bad dream, he used to say, "The dreams speak falsely."(zec.10:2) When he had a good dream, he used to say, Do the dreams speak falsely, seeing that it is written, "I [God] do speak with him in a dream?" (num. 12:6) Raba pointed out a contradiction...There is no contradiction; in one case it is through an angel, in the other through a demon."
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zaqOct 5 '11 at 17:21